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On Galerkin approximations of a quasilinear nonpotential elliptic problem of a nonmonotone type. (English) Zbl 0802.65113
This paper deals with a quasilinear problem whose classical formulation reads: Find $u\in C\sp 1(\overline\Omega)$ such that $u\bigl\vert\sb \Omega\in C\sp 2(\Omega)$ and $-\text{div}(A(x,u)\text{grad }u)+ c(x,u)u= f(x,u)$ in $\Omega$, $u= \bar u$ on $\Gamma\sb 1$, $n\sp T A(s,u)\text{grad }u+ \alpha(s,u) u= g(s,u)$ on $\Gamma\sb 2$. Precise assumption upon the functions are given. The existence and uniqueness of weak and Galerkin solutions are investigated. A heat conduction problem which describes a temperature distribution in large transformers is presented.

65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
35J65Nonlinear boundary value problems for linear elliptic equations
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